Introduction
There are 288 naturally existing nuclei on earth, with 238U being the heaviest among them. Transuranium nuclei, with atomic numbers greater than 92, can only be produced through nuclear reactions [1-3]. The first transuranium nucleus, 239Np was discovered in 1940 among the fission products resulting from bombardment of 238U with thermal neutrons [4]. Since then, nuclear physicists have successfully synthesized 26 transuranium elements artificially by utilizing several types of nuclear reactions. Among these artificial nuclei, transactinide nuclei with Z ≥104 are known as superheavy nuclei (SHNs) [5-7]. These nuclei are located in the northeast region of the nuclear chart and exhibit extreme instability and short half-lives. Nevertheless, the synthesis and study of SHNs are crucial for advancing our understanding of the fundamental properties of nuclear forces, validating nuclear structural models, and extending the periodic table of elements.
Although the SHN region lies at the limits of Coulomb stability, the shell structure effects can influence the fission barrier, thereby contributing to the existence of SHNs. Following the approach proposed by Strutinsky, which involves introducing shell corrections to the liquid-drop model, an “island of stability” at Z = 114 and N = 184 was predicted separately by Sobiczewski et al. and Meldner [8-12]. Further predictions from various microscopic approaches, such as the Skyrme-Hartree-Fock and relativistic mean-field methods, suggest that this “island of stability” could be located at Z = 114, 120, 124 or 126 and N = 172 or 184 [13-15, 16-20]. These theoretical predictions are supported by the observed increase in α-decay half-lives of isotopes with increasing neutron number [8, 21].
The primary mechanism for synthesizing SHNs involves fusion reactions using stable beams and long-lived targets. Early fusion reactions utilizing lighter projectiles and actinide targets were selected to produce superheavy elements (SHEs) with Z = 93 - 106 at LBNL and JINR [22-26]. Subsequent advancements in cold fusion reactions employing 208Pb or 209Bi targets facilitated the synthesis of SHEs with Z = 107 - 113 at GSI and RIKEN [27, 28]. In contrast, hot fusion reactions using 48Ca beams and actinide targets conducted in JINR at Dubna led to the successful synthesis of SHEs with Z = 114 - 118 [29-33]. Currently, the synthesis of new SHEs with Z = 119 - 122 represents a highly competitive frontier in nuclear research.
This review provides a comprehensive overview of the current state of research on the synthesis of SHNs, focusing on both experimental accomplishments and theoretical advancements. We discuss the latest achievements and breakthroughs in the synthesis of SHN, experimental facilities, and theoretical methods employed. Furthermore, this review discusses the challenges encountered in synthesizing new SHN and explores the potential directions for future research.
This article is organized as follows: In Sect. 2, we introduce the discovered SHN and the methods used for their synthesis. Section 3 covers the current experimental facilities, including both existing and under-construction accelerators and separators. In Sect. 4, we discuss the widely applied microscopic and phenomenological models used in theoretical predictions. Section 5 reviews the latest experimental and theoretical advancements in the synthesis of new SHEs. Section 6 addresses the current experimental challenges in synthesizing new SHN and explores potential future developments. Finally, Section 7 provides a summary of this study.
The discovery of superheavy nuclei
Early fusion reactions with C, N, O, Ne, Mg and Ar beams
There are 3386 discovered nuclei of 118 known elements, including 119 artificial SHNs [34]. The discovery of superheavy isotopes began in 1969 at Berkeley, where the fusion reactions 12,13C + 249Cf led to the identification of 257-259Rf [22]. By changing the projectile into 15N and 18O, the elements with Z = 105 and 106 were also synthesized [23, 24]. JINR also independently produced the 104th and 105th elements via reactions 22Ne + 242Pu, 243Am [25, 26]. Additionally, based on the actinide targets 248Cm and 249Bk, researchers have successfully synthesized new superheavy nuclei 260-262Rf and 262Db [35, 36].
In 2000, the reaction 22Ne + 241Am was investigated at the Institute of Modern Physics (IMP) in China, leading to the discovery of 259Db [37]. In 2006, using the reaction 26Mg + 248Cm, 270,271Hs were produced at GSI, with 266,267Sg identified in the α-decay descendants [38, 39]. Most recently, in 2024, JINR researchers employed the reaction 40Ar + 238U, resulting in the synthesis of 273Ds [40]. Experimental results suggest that more asymmetric reaction systems can enhance both the fusion probability and evaporation residue (ER) cross sections when forming the same compound nucleus. For instance, in the 5n-emission channel leading to the formation of 273Ds, the ER cross section for the reaction 34S + 244Pu is 0.4 pb [41], while for the reaction 40Ar + 238U, it is 0.18 pb [40]. Similarly, the fusion cross sections for producing 232Cm and 274Hs via reactions 35Cl + 197Au and 26Mg + 248Cm are higher than those produced through reactions 40Ca + 192Os and 36S + 238U [42-46].
In the early stages of fusion reactions involving extremely asymmetric reaction partners, the formed compound nuclei possess high excitation energies, requiring the evaporation of three to five neutrons to reach the ground state. However, strong competition from fission during the de-excitation process significantly suppressed the yield of the desired nuclei. The limited atomic number of the light projectiles also constrains the atomic number of the SHE that can be synthesized experimentally. Therefore, there is a need to explore new reaction mechanisms to improve the synthesis efficiency of new elements.
Superheavy nuclei produced by cold fusion reactions
In 1974, researchers at JINR explored an alternative reaction mechanism to synthesize new SHNs [47]. By employing 206-208Pb targets and 50Ti and 54Cr projectiles, they discovered new isotopes of 255,256Rf and 260Sg [48, 49]. Because of the reduced mass asymmetry of these reaction systems and the high binding energies of the reaction partners, the excitation energies of the formed compound nuclei were suppressed. This resulted in a de-excitation process requiring the emission of only one or two neutrons, thereby reducing competition from fission. Compared to reactions involving actinide targets and light projectiles, this new reaction mechanism exhibited enhanced ER cross sections. This approach, characterized by low excitation energy and fewer neutron emission, is referred to as “cold fusion reaction”.
Another advantage of cold fusion reactions is that the commonly used 208Pb and 209Bi targets are more readily available in large quantities than actinide targets. In addition, the experimental conditions can be simplified as they are stable target nuclei. Therefore, GSI in Germany had selected this reaction mechanism to investigate the synthesis of new SHEs. In 1981, researchers at GSI managed to synthesize element with Z = 107 via the reaction 54Cr + 209Bi → 262Bh + n [50]. Following this, through the reactions 58Fe+208Pb→265Hs+n, 58Fe+209Bi→266Mt+n, 62,64Ni+208Pb→269,271Ds+n, 70Zn+208Pb→277Cn+n, the SHEs with Z = 108-112 were successfully synthesized [51-55].
Based on the cold fusion reaction, dozens of superheavy nuclei with Z = 104–110 were also synthesized in the GSI [54, 56-61]. In addition, Berkely synthesized 267Ds in the 1n-emission channel of the reaction 59Co+209Bi [62]. The synthesis of 271Ds via the reaction 64Ni+208Pb was also studied by researchers at IMP [63].
In 2004, RIKEN employed the reaction 70Zn + 209Bi and successfully synthesized the element with Z = 113 in the 1n-evaporation channel [27]. However, the ER cross section was only 0.03 pb, which is 107 times smaller than the ER cross section for synthesizing Bohrium. As shown in Fig. 1, there is an exponentially decreasing trend in the ER cross sections as the proton number of the formed compound nucleus increases [64]. This decrease is primarily due to the strong hindrance to the fusion of colliding nuclei caused by increasing Coulomb repulsion [65], as well as the deviation of the deformed subshell with Z = 108 and N = 162 [66, 67]. The synthesis of SHN with
Superheavy nuclei produced by 48Ca-induced hot fusion reactions
To reduce the hindrance caused by Coulomb repulsion, researchers at JINR explored combinations of 48Ca projectile and actinide targets. The selection of 48Ca as a projectile is due to its doubly magic nature with a high binding energy, which enhances fusion probabilities and lowers the excitation energy of the formed compound nuclei. Moreover, the high neutron excess of 48Ca contributes to the formation of neutron-rich compound nuclei. These neutron-rich nuclei tend to exhibit greater stability due to the reduced Coulomb repulsion among protons, a factor that is particularly crucial for superheavy elements, which possess large atomic numbers and therefore significant Coulomb forces acting against their stability.
In Table 1, the characteristics of the three types of fusion reaction are presented. Although the excitation energies in hot fusion reactions are higher than those in cold fusion reactions, leading to a lower survival probability of compound nuclei, the fusion probability in hot fusion reactions is enhanced by the high mass asymmetry of the reaction systems. Additionally, the neutron-rich projectile 48Ca results in the formation of compound nuclei with a higher neutron excess. The increased neutron-to-proton ratio in these compound nuclei enhanced their binding energy and stability.
| Aspect | Early fusion reactions | Cold fusion reactions | Hot fusion reactions |
|---|---|---|---|
| Projectile | Light nuclei with Z=6–18 | Heavy nuclei with Z=22–30 | Double magic nucleus 48Ca |
| Target | Actinide targets | Pb or Bi targets | Actinide targets |
| Excitation energy | Higher, leading to 3–5 neutron emission | Lower, leading to 1–2 neutron emission | Higher, leading to 3–5 neutron emission |
| ER cross section range | From microbarn range to picobarn range | From microbarn range to femtobarn range | Picobarn range |
| Character of products | Neutron-deficient, Z=104–110, less stable | Neutron-deficient, Z=104–113, less stable | Neutron-rich, Z=104–118, potentially more stable |
| Successful synthesis | Elements 104 to 106 | Elements 107 to 113 | Elements 114 to 118 |
The first hot fusion reactions began with the 244Pu target, leading to the discovery of three isotopes of Flerovium, 287-289Fl [68]. Subsequently, elements with Z = 115 - 118 were synthesized using targets of 243Am, 248Cm, 249Bk, and 249Cf, thereby completing the seventh period of the periodic table [29, 31-33, 69]. The maximal ER cross sections for the hot fusion reactions are shown in Fig. 2. This reveals that the maximal ER cross sections increase as the proton number of the formed compound nucleus approaches the predicted shell closure at Z = 114, which is consistent with the increased fission barrier height predicted by macro-microscopic theory [70, 71]. Moreover, a new isotope of element 113 was discovered through the reaction 48Ca + 237Np, with an ER cross section of 0.9 pb, which is an order of magnitude higher than that for synthesizing element 113 via cold fusion reactions [72].
Figure 3 illustrates the SHNs synthesized through three types of fusion reactions, including those identified in the decay products. Compared with the other two types of fusion reactions, hot fusion reactions are particularly effective in synthesizing nuclei with higher proton numbers and greater neutron excess. Consequently, hot fusion reactions have become increasingly favored for the synthesis of new SHNs in recent years.
In 2021, GSI investigated the reaction 48Ca + 242,244Pu and discovered a new isotope, 280Ds, from decay descendants [73]. In 2022, researchers at Dubna identified 286Mc in the 5n-emission channel of the reaction 48Ca + 243Am [74]. In 2023, they explored the reaction 48Ca + 232Th and discovered a new isotope 276Ds, with 272Hs and 268Sg identified among the decay products [75]. This reaction was reattempted in 2024, leading to the discovery of 275Ds in the 5n-emission channel [40].
Experimental facilities
Modern heavy-ion research centers such as HIRFL in China, RIKEN in Japan, GSI in Germany, JINR in Russia, GANIL in France, LBNL, and LLNL in the USA have made significant progress in the synthesis of new isotopes with Z≤ 118 [27, 63, 67, 74, 76-80]. The largest heavy ion research facility in China is HIRFL at IMP [81, 82]. Its accelerator system consists of two cyclotrons (SFC and SSC), a synchrotron (CSRm), and a storage ring spectrometer (CSRe), as depicted in Fig. 4. Typically, the SFC is used as an injector for the SSC. Ions generated by the ion sources are first accelerated by the SFC and then injected into the SSC for further acceleration. The heavy ions provided by both cyclotrons can be accumulated, cooled, and accelerated in CSRm, then extracted to produce radioactive ion beams (RIB) or highly charged heavy ions. These secondary beams are accepted and stored in CSRe for various internal target experiments. In recent years, researchers at IMP have successfully synthesized 38 new nuclei, including 23 heavy and superheavy nuclei, based on HIRFL and other accelerators [83-95].
The UNILAC installed in 1975 at GSI is capable of accelerating all ion species from protons to uranium with energies ranging from 1.4 MeV/u to 11.4 MeV/u [96, 97]. Over the past 40 years, experiments using beams from UNILAC have successfully produced elements with Z= 107–112 and more than four hundred new isotopes [5]. Additionally, UNILAC along with the Heavy Ion Synchrotron SIS18, will serve as a high-current heavy ion injector for the new Facility for Antiproton and Ion Research (FAIR) Synchrotron SIS100 [98, 99].
The linear accelerator RILAC, constructed in 1975 at RIKEN, successfully synthesized approximately 200 new isotopes and made significant contributions to the synthesis and discovery of Nihonium [5, 101]. To facilitate the synthesis of new SHEs with Z=119, RILAC was upgraded to a superconducting linear accelerator system (SRILAC) in 2020 [102, 103]. The beam energy was increased from 5.5 MeV/u to 6.5 MeV/u, enabling SRILAC to play a major role in the synthesis of even heavier new elements.
The Flerov Laboratory of Nuclear Reactions (FLNR) in JINR has produced more than 200 new isotopes using two primary cyclotrons, DC-280 and U-400 [69, 103]. The U-400 accelerator, established in 1979 and continuously upgraded, plays a significant role in the synthesis of elements with Z= 113–118. To further explore the SHE region, DC-280 was developed in 2018, offering beam energies ranging from 4 MeV/u to 8 MeV/u and beam intensities up to 10 p, making it particularly suitable for the synthesis of new SHN [104-106].
The 88-inch Cyclotron Facility at LBNL was first commissioned in 1961 and has been in operation for over six decades. It has played a crucial role in the discovery of more than 600 isotopes [5, 100, 107]. In 2022, the construction of the Facility for Rare Isotope Beams (FRIB) was completed. The superconducting driver linac in the recently developed FRIB at MSU can accelerate the 238U isotope with a beam energy greater than 200 MeV/u, which provides access to the production of thousands of new nuclei [108-111].
Progressive and expansive research in nuclear physics continues to drive the upgradation and modernization of accelerators. The High-Intensity Heavy-Ion Accelerator Facility (HIAF) is a next-generation storage-ring-based heavy-ion facility developed by IMP, with expected completion by 2025 [112, 113]. HIAF integrates a linear accelerator and a synchrotron accelerator to deliver high-energy heavy-ion beams ranging from hydrogen to uranium. The principal goal of HIAF is to synthesize new superheavy nuclei and elements [114, 115]. In parallel, other advanced accelerator facilities, such as the FAIR SIS 100 at GSI, NICA-Booster in Dubna, and EURISOL in Europe, are currently under design and construction [116-118]. The comprehensive beam parameters for these facilities are detailed in Ref. [114].
For the synthesis of a new SHN, the expected ER cross sections are on the order of picobarns, with half-lives ranging from microseconds to several days [119]. The predominant decay modes for these unknown nuclei are predicted to be alpha decay and spontaneous fission. Therefore, decay products are typically separated and implanted into radiation-sensitive Si detectors. The detection of rare alpha-decay events from the synthesized SHN is then carried out against a significant background of side reaction products.
Currently, several kinematic separators have been employed in the study of heavy nuclei. Velocity filter SHIP at GSI and SHELS at JINR are notable examples [120, 121]. These facilities specialize in the separation and identification of heavy nuclei fragments using velocity filtering techniques. In addition, gas-filled magnetic separators, such as DGFRS-2 at JINR, TASCA at GSI, BGS at LBNL, GARIS-II at RIKEN, and SHANS at HIRFL, are employed to enhance the separation and detection of SHEs [122-127]. The detailed design of gas-filled recoil separators is described in Ref. [77]. These separators enable effective separation and high-sensitivity detection, which are critical for advancing the SHE research.
In recent years, the next generation of separators has been gradually put into operation. The GARIS-III at RIKEN was completed as part of an upgrade project in 2020. With enhanced resolution and advanced detector arrays, the aim was to investigate reactions with ER cross sections as low as 10 fb [122, 128]. In 2022, the CAFE2 Program at IMP initiated the development of a new gas-filled recoil separator, SHANS2, as illustrated in Fig. 5. Through a series of performance tests involving the reactions 40Ar + 175Lu, 40Ar + 169Tm, 40Ca + 169Tm, and 55Mn + 159Tb, SHANS2 demonstrated its effectiveness and reliability, highlighting SHANS2 as a critical tool for advancing research in the field of SHE synthesis [129, 130].
Theoretical Models
Currently, experiments aimed at investigating superheavy regions encounter several challenges. The target materials available are rare, expensive, and prone to contamination during experiments. Additionally, the limited beam intensity of accelerators requires long irradiation times, and the expected ER cross sections have already reached the detection limits. As a result, it is necessary to develop theoretical models that can provide precise predictions for optimal projectile-target combinations, incident energies, expected yields, and assess the feasibility of experimental plans.
Based on extensive experimental data, two main types of theoretical approaches have been developed to describe fusion-evaporation reactions. One type is the microscopic models, such as the quantum molecular dynamics (QMD) model [131-133] and time-dependent Hartree-Fock (TDHF) theory [134-138]. The other type is the macroscopic phenomenological models, including the fusion-by-diffusion (FBD) model [134, 139, 140], dynamical cluster-decay model (DCM) [141, 142], two-step model [143-146], statistical model [147], multidimensional Langevin-type dynamical equations [148-151], and dinuclear system (DNS) model [9, 152-161].
Microscopic models
Microscopic models start with basic nucleon-nucleon interactions, often described by effective potentials such as Skyrme potentials. These models require self-consistent field calculations, in which each nucleon moves within the mean field generated by all other nucleons. Microscopic models offer a deep understanding of nucleon behavior and can explain and predict a wide range of nuclear phenomena. However, they often require significant computational resources and are limited by the accuracy of the interaction models.
TDHF theory can be derived from the time-dependent variational principle [162]. In the TDHF, the many-body wave function is approximated as a Slater determinant, automatically ensuring the Pauli exclusion principle. The TDHF method is a fully microscopic, parameter-free theory that unifies the nuclear structure and reactions within a single framework. Dynamic and quantum effects are automatically incorporated into this approach [163].
By constraining the density distribution obtained from the dynamical evolution in the TDHF method, the density-constrained time-dependent Hartree-Fock (DC-TDHF) model can be derived, allowing for the extraction of nucleus-nucleus potentials in heavy-ion reactions. Using this method, Ref. [164] investigated the feasibility of forming a compound nucleus with Z=119 via the 50Ti+249Bk reaction.
The TDHF model can also be combined with phenomenological models to obtain more accurate predictions. In Ref. [165], the isotopic dependence of quasi-fission and fusion-fission in the production of flerovium isotopes was investigated. The TDHF method was applied for fusion and quasifission dynamics, while the statistical evaporation model HIVAP was used for fusion-fission dynamics. Reference [134] examined the orientation effects of the 48Ca+238U reaction with the reaction dynamics described by TDHF theory, as illustrated in Fig. 6. This study combines the TDHF model with coupled-channel and FBD models, and predicts that the tip orientation is more favorable for both the capture process and formation of the compound nucleus in this reaction. Additionally, Ref. [137] combined the TDHF method with the Langevin equation, suggesting that differences in the probabilities of evaporation residue formation among reaction systems primarily originate from the evaporation process, which is sensitive to the fission barrier height and excitation energy of the compound nucleus.
The QMD model is a microscopic model derived from the classical molecular dynamics (CMD) model and the many-body Schrödinger equation [166]. In the QMD model, each nucleon is represented by a Gaussian wave packet, incorporating both mean-field effects and two-body collisions [167]. Advanced variations of the QMD model, such as the isospin-dependent quantum molecular dynamics (IQMD) model and the improved quantum molecular dynamics (ImQMD) model, are particularly effective in describing the processes of low-energy heavy-ion collisions.
Within the QMD model framework, the fusion process is considered to occur when two independent nuclei successfully overcome the Coulomb barrier and maintain a stable monomer density during rotation or oscillation of the compound nucleus. By simulating a large number of events, the fusion cross section at a specific incident energy can be statistically determined. In Ref. [131], the excitation functions predicted by the ImQMD model for the reaction 48Ca+208Pu were compared with the results obtained from the DNS model and experimental data, as depicted in Fig. 7. This work confirmed the reliability of the ImQMD model and predicted the optimal projectile-target combinations for synthesizing 243-248No isotopes. Additionally, Ref. [133] applied the IQMD model to investigate the enhanced fusion probabilities in reactions with 44Ca beams, attributing the enhancement to the rapid development of the neck region and the higher neutron-to-proton ratio. The study also predicted the optimal projectile-target combinations for producing new 245-250Lr isotopes, along with the corresponding incident energies.
Phenomenological models
In phenomenological models, dynamical evolution equations are established by incorporating certain collective degrees of freedom to describe the dynamics of nuclear reactions. These approaches simplify the computational process by neglecting the intricate interactions among the nucleons. With the de-excitation process treated using statistical models, the HIVAP code, the KEWPIE code or the GEMINI++ model [143, 168-171], phenomenological models can be effectively applied to heavy-ion collision reactions near the Coulomb barrier.
One approach for describing the fusion process considers the dynamic evolution of the formed mononucleus, proposing that once the projectile and target nuclei come into contact, they rapidly lose their individuality and form a highly deformed nucleus. Fusion is considered to occur when the deformed nucleus gradually evolves into a spherical compound nucleus; otherwise, quasi-fission occurs. The macroscopic dynamical model was the first to describe the fusion mechanism based on this concept [172-175]. In this model, the nucleus is treated as a viscous liquid drop, and the fusion process is regarded as a purely dynamic phenomenon that can be described using classical equations of motion. However, this model faced challenges in reproducing the ER cross sections for fusion reactions, as it did not account for the competition between fusion and quasi-fission, nor did it incorporate the shell effect [176]. To address these limitations, the two-step model [143-145, 177] and fusion-by-diffusion model [139, 140] introduced shell effects in the calculation of the potential energy surface, along with statistical fluctuations in the interaction of colliding nuclei [178]. These enhancements have allowed for more accurate reproduction and prediction of ER cross sections in fusion reactions.
Another description of the fusion process focuses on the degree of freedom of the mass asymmetry. In these models, the two nuclei retain their individuality and nucleon transfer occurs within the formed dinuclear system, as depicted in Fig. 8. Fusion is considered to occur when all the nucleons from the projectile are successfully transferred to the target nucleus. Conversely, quasi-fission process takes place when nucleons are transferred from the target nucleus to the projectile [179].
Based on this assumption, the DNS model was developed. The nucleon transfer process within the DNS model is treated by solving a set of master equations, which are governed by the potential energy surface considering nuclear structure effects [154]. The calculated results for cold and hot fusion reactions using the dinuclear system model match well with available experimental data [157, 180]. However, this approach initially did not consider the dynamic factors influencing the fusion stage. To address this, Ref. [153] coupled the dynamic deformation of the nucleus with nucleon transfer within the DNS model, and predicted the ER cross sections for the synthesis of a new SHE. In recent years, neural networks and machine learning methods have been introduced to optimize nuclear data and refine the parameters of the theoretical model [181-184].
The nucleon collectivization model offers an intermediate approach for describing the fusion process compared with the previously mentioned methods [185]. In this model, within the formed dinuclear system, a portion of nucleons is considered to become “common” nucleon, shared by both nuclei. Fusion is thought to occur when all nucleons are transformed into common nucleons; otherwise, quasi-fission occurs. Although this model successfully describes the excitation function of hot fusion reactions, the physical concept of the introduced common nucleons remains highly controversial.
Given the significant difference in the descriptions of the fusion process across various models, some researchers have attempted to combine fusion mechanisms from different theoretical models and experimental observations to develop relatively simple empirical formulas for calculating fusion probability [186-191]. These formulas, informed by experimental phenomena and theoretical approaches, identify several influential factors in the fusion process, including the excitation energy, quasi-fission barrier, compound nucleus mass or charge number, and mass asymmetry [186, 188, 189]. These empirical formulas effectively reproduce the experimental results of the known fusion reactions. Recently, a model-independent method, based on the Coulomb barrier height of side-side collisions and Q value, was established to predict the optimal incident energies for unknown reaction systems [192]. This approach allows the estimation of optimal incident energies with minimal uncertainty.
Efforts in the Synthesis of New Superheavy Elements with Z = 119, 120
Since the synthesis of Oganesson through the reaction 48Ca+249Cf→294Og+3n, the seventh period of the periodic table was completed. However, for the synthesis of SHE with atomic numbers Z > 118, the 48Ca-induced fusion reactions are restricted by the limited availability of Einsteinium and Fermium targets. Consequently, heavier beams, such as 50Ti, 51V, and 54Cr, must be applied.
The experimental attempts to synthesize a new SHE are summarized in Table 2. Initially, GSI attempted to synthesize the SHE with Z=120 using the reaction 64Ni + 238U in 2008 [193], and JINR attempted the reaction 58Fe + 244Pu in 2009 [194]. However, no corresponding α decay chains were observed in these experiments. In 2016, GSI attempted to synthesize element with Z=120 via the reaction 54Cr + 248Cm [195, 196], observing three α decay chains attributed to 299120. Unfortunately, these were later identified as random events [197]. Additionally, in 2020, GSI conducted experiments to search for the new elements with Z = 119 and Z = 120 using the reactions 50Ti + 249Bk and 50Ti + 249Cf, respectively, but no evidence of a new SHE was found [198]. In 2022, RIKEN investigated the quasielastic barrier distribution for the reaction 51V+248Cm and deduced the optimal reaction energy for synthesizing element with Z = 119 through this reaction [199].
| Element | Year | Laboratory | Reaction | Results | Detection limit | Ref |
|---|---|---|---|---|---|---|
| Z = 120 | 2008 | GSI | 64Ni + 238U | No α decay chain | 0.09 pb | [193] |
| Z = 120 | 2009 | JINR | 58Fe + 244Pu | No α decay chain | 0.4 pb | [194] |
| Z = 120 | 2016 | GSI | 54Cr + 248Cm | Three random α decay chains | 0.58 pb | [195] |
| Z = 119 | 2020 | GSI | 50Ti + 249Bk | No α decay chain | 0.065 pb | [198] |
| Z = 120 | 2020 | GSI | 50Ti + 249Cf | No α decay chain | 0.2 pb | [198] |
| Z = 119 | 2022 | RIKEN | 51V + 248Cm | Optimal reaction energy was estimated | [199] |
In 2024, the reaction 50Ti+244Pu was investigated at the LBNL 88-Inch Cyclotron Facility, producing an isotope 290Lv with an ER cross section of 0.44 pb [200]. Although the ER cross section is lower than that of the 48Ca-induced reactions, this experiment proves the feasibility of using a 50Ti beam for the production of a new SHE [201]. Recently, the upgraded experimental facility HIFRL-CAFE2 was tested using the reaction 48Ca + 243Am. The synthesis of the element with Z = 119 via the reaction 54Cr + 243Am is currently underway. JINR has also planned to explore the reactions 50Ti + 249Bk and 54Cr + 243Am for synthesizing the 119th element, as well as the reactions 50Ti + 249Cf and 54Cr + 248Cm for the 120th element [202]. The nuclei to be searched are summarized in Fig.9.
Various theoretical models have predicted the optimal projectile-target combinations and corresponding incident energies for new elements beyond Oganesson via fusion reactions [140, 142, 143, 153, 157, 188, 189, 203-210]. Figure 10 shows the optimal reaction energies predicted in Ref. [157] and estimated by RIKEN for the reaction 51V + 248Cm, with a strong agreement between the predicted and estimated energies. As summarized in Ref. [157] and Ref. [200], most models identify the reactions 50Ti + 249Bk and 50Ti + 249Cf as advantageous for producing SHE with Z = 119 and Z = 120. The predicted maximal ER cross sections from different models generally fall within the fetobarn range, although the optimal incident energies can differ by several MeV for certain reactions. Additionally, based on measurements of the mass and angular distributions of fission fragments, Ref. [211] also predicted that the reaction 50Ti + 249Cf shows promise for synthesizing SHE with Z = 120. For the synthesis of SHE with Z = 121, Ref. [156] suggested that the reactions 46Ti + 252Es and 46Ti + 254Es could be feasible in future experiments, with maximal ER cross sections expected to reach several fetobarns.
Recently, researchers proposed high-energy alpha particle emission as a novel mechanism for synthesizing new elements [212]. In the experiments conducted at JINR, the energy spectra of α particles emitted from the reactions 40Ar + 232Th and 48Ca + 238U at near-barrier energies were measured. The results indicated that at the kinematic limit, the observed cross sections were in the picobarn range. These experiments revealed that two-body reactions facilitate the production of heavy residue nuclei with minimal excitation energy, thereby enhancing their survival probability. Consequently, this reaction mechanism can potentially produce SHN with ER cross sections that are several orders of magnitude greater than those achieved through traditional fusion-evaporation reactions.
Current Challenges and Future Directions
The synthesis of new SHNs faces several challenges, including short half-lives and high instability of both the target materials and the produced nuclei [213, 214]. The maximal ER cross sections in the hot fusion reactions also approached the detection limit. Moreover, the limited availability of actinide targets requires the use of heavier projectiles in future experiments [200], which is expected to further suppress ER cross sections compared to those induced by 48Ca. To address these challenges, nuclear physics laboratories worldwide are upgrading their equipment, as discussed in Sect. 3, to achieve higher beam intensities and enhanced detection precision.
In various theoretical models, many assumptions and approximations have been adopted, such as employing the double-folding potential with a sudden approximation to calculate the nuclear potential, assuming quadrupole or hexadecapole deformations of the nucleus, and using empirical surface diffusion coefficients. The fission barrier in the de-excitation process is typically described in one-dimensional parameterized form. Precise nuclear masses of superheavy nuclei are also crucial [215-217]. As demonstrated in Refs. [218, 219], even predictions made using the same model can vary significantly when based on different mass tables.
Although these assumptions and approximations are necessary because of the current limitations in computational resources and theoretical development, the uncertainties introduced by empirical parameters and approximations constrain the extrapolative capability of the models and cannot be ignored. Some studies have attempted to estimate the uncertainties originating from these empirical parameters or to constrain them using microscopic approaches [146, 157, 158, 220]. However, a comprehensive evaluation of the uncertainties introduced by these empirical methods is required.
Calculations in the SHN region using microscopic models involve handling the interactions among a large number of nucleons, often resulting in computation times ranging from several months to years. This limitation significantly restricts the application of microscopic models in SHE research. While advancements in computational power, as predicted by Moore’s law, may alleviate this issue, the introduction of new parallel computing methods presents a more immediate solution. Researchers are exploring ways to identify the key physical degrees of freedom in nuclear reactions to develop new phenomenological models. Additionally, the limited amount of experimental data from 48Ca-induced reactions hinders the verification of theoretical models, raising concerns regarding their reliability when extrapolating to reactions involving heavier projectiles. More experimental data from a variety of projectile-target combinations are also needed to develop more robust theoretical models.
Currently, α decay tagging is the primary technique for identifying reaction products, but it is limited by the requirement that synthesized nuclei have suitable half-lives and unambiguous decay chains. As a result, many SHNs in the neutron-rich region cannot be identified using this method. Therefore, new identification techniques, such as high-precision mass measurements, laser resonance ionization, and a combination of mass separation with decay tagging, should be considered [221-223].
The relatively low neutron-to-proton ratio in both the projectile and target nuclei during the fusion reactions leads to the formation of a compound nucleus with a reduced neutron number. Additionally, the compound nucleus must undergo neutron evaporation to reach its ground state, resulting in the production of nuclei that are typically neutron-deficient. Such conditions present a significant challenge for the production of neutron-rich superheavy nuclei, as the heaviest available targets are currently 249Cf and 249Bk.
The actinide target nuclei used in fusion reactions are produced through the intense neutron irradiation of targets composed of mixed Pu, Am, and Cm in high-flux reactors, as illustrated in Fig. 11. Currently, reactors capable of providing these actinide materials include the High Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory [224], the Advanced Test Reactor (ATR) at Idaho National Laboratory [225], and the SM-3 Reactor at the Research Institute of Advanced Reactors (RIAR) in Dimitrovgrad [226]. Additionally, the Jules Horowitz Reactor (JHR) [227] and the Tsinghua High Flux Reactor (THFR) [228], which are currently under construction, will also provide heavy actinide targets. In future experiments, new actinide target materials, particularly neutron-rich targets, such as 251Cf and 254Es, could be produced and applied in fusion reactions [202].
Theoretical studies suggest an “island of stability” where enhanced shell effects lead to long-lived nuclei. However, the precise location of this area remains uncertain because of the varying predictions from different nuclear models. Macroscopic-microscopic models employing different potentials, such as Nilsson, Woods-Saxon, and folded Yukawa, typically locate the center at Z = 114, N = 184 [11, 12, 229, 230]. Depending on the selected parameters, self-consistent models using Skyrme-Hartree-Fock or relativistic mean field interactions predict various combinations of Z = 114, 120, 124, or 126, and N = 172 or 184 [14, 15, 15-20]. In recent years, researchers have been investigating novel reaction mechanisms to explore the neutron-rich superheavy region and reach the center of the “island of stability”. Radioactive beam-induced fusion reactions have been proposed as methods for synthesizing neutron-rich SHN [159, 190, 222, 231, 232]. Additionally, multi-nucleon transfer (MNT) reactions have been suggested as promising approaches for producing neutron-rich isotopes [1-3, 222, 232-238].
Radioactive beams
Compared to stable beams, neutron-rich radioactive projectiles have higher neutron-to-proton ratios, enabling exploration of the neutron-rich SHN region. Figure 12 summarizes the possible radioactive beams that can be generated at the Argonne Tandem Linac Accelerator System (ATLAS). However, a significant challenge for radioactive beam-induced fusion reactions is low beam intensity. Although stable beam intensities can reach the order of 1012 p/s, the intensities of radioactive beams are currently much weaker. To address this limitation, modern radioactive beam accelerator facilities, such as the Radioactive Isotope Beam Factory (RIBF) and the Second-generation System On-Line Production of Radioactive Ions (SPIRAL2) [239, 240], are working on upgrading their capabilities to achieve high-intensity exotic ion beams [222, 241].
Many theoretical studies have investigated the mechanisms of radioactive beam-induced fusion reactions. Reference [242] predicted that the reaction induced by the neutron-rich radioactive beam 46Ar could produce new neutron-rich nuclei 290-292Fl, provided that the beam intensity was sufficient. Reference [159] explored the production of neutron-rich SHN with Z = 105–118 through radioactive beam-induced fusion reactions. Additionally, Ref. [243] examined the possibility of reaching the “island of stability” via radioactive beams and 244Pu, 248Cm, 249Cf targets.
Multi-nucleon transfer reactions
Several MNT reaction experiments have been conducted in recent years. In 2018, significant α particle emission was observed in the reaction 238U + 232Th [244]. A comparison between the experimental results and theoretical calculations suggested the possible formation of unknown neutron-rich nuclei with atomic numbers of up to 116, as depicted in Fig. 13. However, owing to limitations in the detection methods, the cross section information for these formed nuclei was not measured. Significant advancement in the production of new nuclei via MNT reactions was achieved in 2015 at the UNILAC accelerator at GSI, where the reaction 48Ca+248Cm was studied. This experiment resulted in the identification of five new neutron-deficient isotopes: 216U, 219Np, 223Am, 229Am and 233Bk [245]. These findings demonstrate that the MNT reactions can be effectively utilized to synthesize neutron-deficient transuranium nuclei. In 2023, RIKEN discovered a new neutron-rich nucleus, 241U, through the MNT reaction 238U + 198Pt, demonstrating the feasibility of MNT reactions for producing neutron-rich nuclei near the N = 152 subshell [246].
Several theoretical models, such as the DNS model [6, 247-251], GRAZING model [252-254], QMD model [252, 255, 256], Langevin equations [257, 258], time-dependent covariant density functional theory [259], and TDHF model [256, 260-264] have also been applied to investigate MNT reactions. In Ref. [265], the reliability of DNS model in MNT reactions was validated, predicting the production cross sections of four new Rf isotopes through the 238U + 252Cf reaction. Reference [266] combined the GRAZING model framework with the DNS model, significantly enhancing the theoretical descriptions of experimental results for MNT reactions. Reference [267] introduced the deformation degree of freedom and Monte Carlo de-excitation methods, leading to the development of an improved DNS-sysu model, and explored the feasibility of reaching the “island of stability” through radioactive-beam induced fusion reactions and MNT reactions, as shown in Fig. 14.
Based on the ImQMD model, Ref. [268] studied the production cross sections of superheavy isotopes formed in the 238U + 238U reaction, finding that the isospin dependence of the fission barrier results in production cross sections for neutron-rich isotopes 254-256Cf being nearly three orders of magnitude lower than those of 249Cf. Ref. [252] presents a comparison of the mass distributions of primary binary fragments predicted by the ImQMD, DNS, and GRAZING models with experimental data, as shown in Fig. 15. The study reveals that the DNS and GRAZING models are primarily suitable for describing transfer processes involving only a few nucleons between the projectile and target. In contrast, the ImQMD model shows a high level of agreement with experimental results across most mass regions.
For the TDHF model, Ref. [262] observed that in the 238U + 124Sn reaction, owing to the inverse quasifission process, 124Sn can transfer a large number of nucleons to 238U, leading to the formation of new isotopes. By employing a multidimensional dynamical model based on Langevin equations, Ref. [269] explored the production of heavy transuranium nuclei during collisions with actinide nuclei. The results suggest the feasibility of synthesizing several neutron-rich heavy actinide isotopes, with production cross sections surpassing 1 μb. Additionally, new methods based on the master and Langevin equations have been applied to MNT reactions [270, 271]. The feasibility of MNT reactions with radioactive beams has been investigated in several studies [272-275].
Summary
The search for new superheavy nuclei achieved significant success, particularly with the completion of the seventh period of the periodic table. Despite these accomplishments, the synthesis of elements beyond Z = 118 remains a substantial challenge, largely because of the limited availability of actinide targets and rapidly decreasing ER cross sections. Employing heavier projectiles is a promising approach for the synthesis of new superheavy elements. The feasibility of the 50Ti projectile is experimentally validated. The investigation of new reaction mechanisms, including radioactive beam-induced fusion and multi-nucleon transfer reactions, presents promising pathways for producing neutron-rich superheavy nuclei and for approaching the next shell closure. Recent developments in theoretical models have provided valuable predictions for optimizing experimental conditions. However, the reliability of these models requires further validation. Continued upgrades to accelerator beam intensities and detector efficiencies, coupled with the development of more precise theoretical models, will be crucial for overcoming the challenges associated with the synthesis of new superheavy elements.
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